Rice University Department of Mathematics Colloquium

Dense subgroups of simple Lie groups

4:00 pm Friday, October 14th, 2016
Yves Benoist (Université Paris-Sud)

Abstract: Let G be a Lie group. We will focus on the following two questions. Is the Hausdorff dimension of a Borel measurable, dense and proper subgroup of G always zero? Is the convolution of sufficiently many continuous functions on G always continuously differentiable? Even though the answer to these questions is NO when G is abelian the answer is YES when G is simple. This will follow from a local spectral gap property. Joint work with N. de Saxce.

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